Extreme Events: a consequence of a crisis

J.TREDICCE, ALEJANDRO HNILO, M.KOVALSKY, C.METAYER, T.QUINIOU, J.RIOS LEITE

Singapur

Conferencia; IPS15 Conference; 2015

IPS15 Conference

Rogue waves, earthquakes of high magnitude, financial crises, tsunamis, epileptic seizures have they any common feature other than their catastrophic and undesirable character? Yes! they are extreme events. Extreme events are often called disasters as they correspond to significant and abrupt changes (damages) of our environmental and socio-economic conditions. Nowadays the growing toll of damages from extreme events around the world leads to unprecedented economic losses and then presents a high challenge for public policy and scientific research. One of the main objectives of studying extreme events is to provide knowledge and tools that can contribute to the reduction of vulnerability. Greater attention is now paid to their causes and their study includes observation, statistics and prediction, in particular due to the rising societal exposure. It is then important to identify laboratory systems producing such ?catastrophic events? in some controllable way. Here we propose to study the nonlinear dynamics of a class-B laser with loss modulation, described by very simple equations and try to identify the appearance of optical rogue waves. The laser can be modelled by dS/dt = - S (1 + m cos(ωt) ? N) (1) dN/dt = -Γ (N -A + S N) (2) where the time is in units of the photon lifetime, S and N are the photon and population inversion respectively, Γ is the ratio of the population to the photons lifetimes, A is the pump parameter, and m and ω are the amplitude and frequency of the modulation respectively. Through analysis of bifurcation diagrams of the maxima of intensity, Smax, as a function of a parameter m, we show that after reaching chaos, chaotic attractors expand abruptly in phase space. Furthermore, just before reaching a fully developed chaos, it is possible to observe the coexistence of a chaotic and periodic attractors at low m values. We noticed that the trajectory in phase space spends most of time in a dense region of the strange attractor, only occasionally performing a long excursion, resulting in a high pulse. Then such high intensity pulses are extreme events in the chaotic behaviour and their appearance generates a long tail in the probability distribution of the maxima of intensity. We determine that such extreme events appear only after a collision of the chaotic attractor with an unstable orbit. The collision is a bifurcation of the chaos called external crisis. Then the extreme events are direct consequence of a crisis as indicated in the title of this presentation. The theoretical results are compared to experimental data obtained from a solid state laser with electro